“Historical Experience and Challenges of Proceedings of 13th Baltic Sea Geotechnical Conference Geotechnical Problems in Baltic Sea Region” ISSN 2424-5968 / ISBN 978-609-457-957-8 Lithuanian Geotechnical Society eISSN 2424-5976 / eISBN 978-609-457-956-1 Lithuania, 22–24 September 2016 DOI: http://doi.org/10.3846/13bsgc.2016.010

© 2016 The Authors. Published by VGTU Press. This is an open-access article distributed under the terms of the Creative Com-mons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Direct Shear Test: Normal and Tangential Stresses Evaluation According to Constant and Variable Shearing Area

Šarūnas Skuodis1, Arnoldas Norkus2 Geotechnical Engineering Department, Faculty of Civil Engineering,

Vilnius Gediminas Technical University, Vilnius, Lithuania E-mails: 1sarunas.skuodis@vgtu.lt (corresponding author); 2arnoldas.norkus@vgtu.lt

Abstract. Investigations of soil shear strength properties for Baltic Sea shore sand along Klaipėda city is presented. Investi-gated sand angle of internal friction (φ) and cohesion (c) is determined via two different direct shear tests procedures. First procedure is standard and ordinary in geotechnical practice, when direct shear test is provided using constant shearing area. Second test procedure is different because shearing area according to horizontal displacement each test second is recalculated and reducing during horizontal movement. According to these two different testing procedures provided comparison of normal and tangential stresses. Keywords: variable shearing area, direct shear test, normal stress, tangential stress, angle of internal friction, peak shearing strength, residual shearing strength. Conference topic: Soil and rock investigation.

Introduction The decision whether to use peak or residual shear strengths (Fig. 1) for a stability analysis must be made in the context of a specific design situation. In general, if there are potential construction, operation, or design con-ditions that might cause relative displacement between layers, then a post-peak or residual shear strength for the layer having the lowest peak strength is appropriate.

Fig. 1. Example graph of shear force or shear stress versus

horizontal displacement (Thiel 2001)

Knowing, that shearing strength parameters de-pends on normal and tangential stress values (Khalil-moghadam et al. 2009; Havaee et al. 2015; Kimura et al. 2015; Wang et al. 2015) it was made a decision to evalu-ate variable shearing area (Naranjo et al. 2014; Skuodis, Tamošiūnas 2014; Taheri et al. 2015; Takano et al. 2014) during direct shear test.

Methodology of direct shear test For investigations it was used sand from the North part of Klaipėda city in Giruliai at the Baltic Sea coast. The average density of particles (ρs) varies from 2.65 to 2.67 g/cm3. Sample density (ρ) varies from 1.49 to 1.51 g/cm3. Sand mineralogical composition consists ba-sically of dominating ingredients, namely: ~85% silica and ~6% sunstone with remaining contribution of carbo-nate, mica and other minerals. Uniformity coefficient CU = 1.47, coefficient of curvature CC = 0.93 was ob-tained for investigated sand.

Used direct shear test is standard (Lane, Vanapalli 2002). Main difference of new testing methodology from standard one – recalculation of normal and tangential stress during direct shear test according to horizontal shearing ring movement u (Fig. 2).

Standard direct shear test procedure is runned ac-cording to these steps: a) vertical stress loading up to cho-sen maximum stress and keeping constant vertical stress all testing procedure; b) establishment of horizontal bottom shearing ring movement with loading ramp 0.50 mm/min up to maximum load 9.00 mm (Skuodis 2015).

Improved testing procedure is same as the standard one except the fact, that during horizontal movement each second is recalculated vertical and tangential stresses according to variable shearing area (Nguyen 2015).

In this case it is evaluated actual vertical and tan-gential stresses during testing. Variable shearing area is obtained by (1) formulae.

,2)]))cos(sin(25.0[(

)]cos(360)5.0([2 0

2

⋅⋅⋅⋅

−⋅⋅⋅

⋅=

dduau

duadA π

(1)

Skuodis, Š.; Norkus, A. 2016. Direct shear test: normal and tangential stresses evaluation according to constant and variable shearing area

94

where: d – sample diameter, mm; u – horizontal displace-ment, mm.

Peak shearing strength is obtained according to τ/σn = max. Residual shearing strength is obtained evalu-ating results from peak shearing strength till the end of testing procedure according to τ/σn = min. Normally low-est tangential and vertical stress ratio is obtained, when horizontal displacement is around 9.00 mm (Thiel 2001). For vertical and tangential force measurements it was used S – type full bridge load transducers (Lamande et al. 2015).

Fig. 2. Graphical explanation of constant and

variable shearing area

Analysis of obtained results

As it was mentioned above, all direct shear tests was ac-complished according to two different shearing method-ologies. First of all, it is presented normal vertical stress and tangential stress analysis under peak and residual shearing strength (Table 1). Purpose of this comparison – reveal the difference of normal vertical stresses and tan-gential stresses, when testing procedure is accomplished according to variable shearing area. For this reason, cal-culated normal stresses and tangential stresses, according to constant shearing area is having lower stresses values in comparison with obtained according to variable shear-ing area.

Analysis of peak shearing strength normal stresses obtained according to constant and variable shearing area on average differs 11.41%. The same difference obtained for tangential stresses under peak shear strength compar-ison. Comparing residual shearing strength stresses – dif-ference between constant and variable shearing area nor-mal stresses on average is 18.37% and 18.58% for tangential stresses.

Obtained normal and tangential stresses differences at the peak shearing strength is not so big (11.41%) that could make a very huge influence for soil testing results. Peak shearing strength angle of internal friction obtained according to constant shearing area is φ = 28.75º and ac-cording to variable shearing area φ = 28.77º. This fact al-lows to run direct shear test without direct evaluation of variable shearing area during test procedure.

Table 1. Peak and residual shearing strength analysis according to constant and variable shearing area

Peak shearing strength Residual shearing strength Constant shearing area Variable shearing area Difference, % Constant shearing area Variable shearing area Difference, %

σn, kPa τ, kPa σn, kPa τ, kPa Δ σn Δτ σn, kPa τ, kPa σn, kPa τ, kPa Δ σn Δτ 89.90 54.94 100.14 61.20 11.39 11.39 87.87 47.26 102.59 55.18 16.75 16.76 90.98 54.48 100.77 60.34 10.76 10.76 89.23 46.19 104.69 54.20 17.33 17.34 84.96 62.59 92.18 67.91 8.50 8.50 87.21 43.84 104.27 54.00 19.56 23.18 82.50 47.74 97.79 56.58 18.53 18.52 85.36 48.80 101.25 57.89 18.62 18.63 86.21 46.41 99.93 53.80 15.91 15.92 83.65 37.23 99.33 44.21 18.74 18.75 89.57 58.54 99.38 64.95 10.95 10.95 89.96 49.50 106.74 58.74 18.65 18.67 181.16 95.69 199.75 105.51 10.26 10.26 169.27 81.30 200.80 96.44 18.63 18.62 184.54 121.39 200.55 131.93 8.68 8.68 168.75 101.69 200.24 120.67 18.66 18.66 181.22 103.54 199.84 114.17 10.27 10.27 168.06 85.88 199.39 101.90 18.64 18.65 181.62 98.69 200.46 108.93 10.37 10.38 169.27 84.52 200.81 100.27 18.63 18.63 182.37 99.69 199.86 109.25 9.59 9.59 168.12 84.81 199.42 100.60 18.62 18.62 181.86 106.08 199.69 116.48 9.80 9.80 168.55 86.75 199.82 102.84 18.55 18.55 271.39 167.03 300.21 184.77 10.62 10.62 253.34 141.96 300.11 168.17 18.46 18.46 268.96 152.06 299.85 169.52 11.48 11.48 252.48 132.25 299.42 156.83 18.59 18.59 264.84 168.34 300.50 191.01 13.46 13.47 254.05 155.20 300.64 183.67 18.34 18.34 270.19 142.38 299.80 157.99 10.96 10.96 254.86 127.84 300.51 150.74 17.91 17.91 270.12 146.79 300.62 163.37 11.29 11.30 256.47 129.69 301.14 152.28 17.42 17.42 266.77 145.53 300.12 163.73 12.50 12.51 252.63 110.01 299.57 130.45 18.58 18.58

Skuodis, Š.; Norkus, A. 2016. Direct shear test: normal and tangential stresses evaluation according to constant and variable shearing area

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Examining residual shearing strength obtained angle of internal friction according to constant shearing area is φ = 27.66º and according to variable shearing area φ = 27.61º. In this case even almost 20% difference of normal and tangential stresses difference obtained by constant and variable shearing areas is not having influ-ence for shearing strength results.

In both cases, when it is analysed peak and residual shearing strength obtained difference of angle of internal friction according to constant and variable shearing var-ies from 0.02º to 0.05º. Variety appears, because angle of internal friction changes (Bareither et al. 2008) according to used low and/or high normal vertical stress during test-ing procedure (Huang et al. 2015; Senatore, Iagnemma 2011; Kang 2014; Kang et al. 2015).

Detailed peak shearing strength comparison accord-ing to constant and variable shearing area is given in Fig-ure 3. Residual shearing strength comparison with two different shearing parameters evaluation methodologies is given Figure 4.

Fig. 3. Peak shearing strength comparison according

to constant and variable shearing area

Fig. 4. Residual shearing strength comparison according to constant and variable shearing area

Fig. 5. Tangential stress versus horizontal displacement:

continuos line – variable shearing area; dot line – constant shearing area

Direct shear tests results given in Figures 3 and 4 once again showing, that angle of internal friction is prac-tically the same if it is compared constant and variable shearing area testing methodologies. Nevertheless, in both figures (Figs 3–4) it is clearly seen normal and tan-gential stresses differences of two different testing meth-odologies, especially stresses differences increases, when analyzing residual shearing strength (Fig. 4).

As an example on stresses differences it is presented tangential stress path diagram according to horizontal displacement testing the same soil with constant normal vertical stress σn = 100; 200 and 300 kPa (Fig. 5).

In Figure 5 given tangential stresses differences clearly shows, that these differences increases according to horizontal displacement increment and normal vertical stress value – at big displacements and higher normal vertical stresses tangential stresses difference are bigger (~20%).

Conclusions A series of direct shear tests were conducted for normal and tangential stresses evaluation according to constant and variable shearing area. Analysis of stresses differ-ences provided at the peak and residual shearing strength. Following findings were drawn from this study:

1) Normal and tangential stress at the peak shearing strength according to variable shearing area is 11.41% higher than comparing with obtained according to con-stant shearing area;

2) Normal and tangential stress at the residual shear-ing strength according to variable shearing area is ~18.5% higher than comparing with obtained according to constant shearing area;

3) Implementation of variable shearing area into di-rect shear test procedure does not have any influence for angle of internal friction. Variable shearing area helps only to evaluate more accurate normal and tangential stresses;

4) All these conclusions can be applied only for di-rect shear tests provided with controlled vertical stress. Small difference of stresses comparison can appear, be-cause not for all sands peak and residual shearing strength is obtained at the same horizontal displacement.

τ = 0,5487σn + 5,5565τ = 0,5491σn + 6,0684

0

50

100

150

200

250

0 100 200 300 400

τ, kPa

σn, kPaConstant shearing areaVariable shearing areaLinear (Constant shearing area)Linear (Variable shearing area)

τ = 0,5242σn – 0,5010τ = 0,5230σn – 0,2514

0

50

100

150

200

0 100 200 300 400

τ, kPa

σn, kPaConstant shearing areaVariable shearing area

0

50

100

150

200

0 2 4 6 8 10

τ, kPa

u, mm

Skuodis, Š.; Norkus, A. 2016. Direct shear test: normal and tangential stresses evaluation according to constant and variable shearing area

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For tests conducted according to constant volume it is necessary to provide another research study.

Acknowledgements An equipment and infrastructure of Civil Engineering Research Centre of Vilnius Gediminas Technical Univer-sity was employed.

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